The R Spatial Ecosystem

A few main packages are dedicated to spatial data handling like import/export, display, geoprocessing, spatial ststistics.

“Historical” Packages

rgdal: interface between R and GDAL (Geospatial Data Abstraction Library) and PROJ4 libraries: raster / vector geospatial data formats and coordinate transformation.
sp: classes and methods for spatial data in R.
rgeos: interface between R and GEOS (Geometry Engine - Open Source) library: area, perimeter, distances, dissolve, buffer, overlap, union, contains…

These packages are still widely used.

Simple Features for R

sf Website: Simple Features for R
First release: October 20, 2016
sp, rgeos and rgdal functionnalities in one package.
Easier data handling, simpler objects.
Tidy data: compatibility with the pipe synthax and tidyverse operators.
Main author and maintainer: Edzer Pebesma (also sp author)

sf objects data structure:

format sf

Using `sf`

Data Import

library(sf)
mtq <- st_read("../data/mtq/martinique.shp")

Reading layer `martinique' from data source `C:\Users\kim.antunez\Desktop\Florence_R\flo\data\mtq\martinique.shp' using driver `ESRI Shapefile'
Simple feature collection with 34 features and 23 fields
geometry type:  POLYGON
dimension:      XY
bbox:           xmin: 690574.4 ymin: 1592426 xmax: 736126.5 ymax: 1645660
epsg (SRID):    32620
proj4string:    +proj=utm +zone=20 +datum=WGS84 +units=m +no_defs

Data Display

Default

plot(mtq)

Only geometry

plot(st_geometry(mtq))

Centroids Extraction

mtq_c <- st_centroid(mtq)
plot(st_geometry(mtq))
plot(st_geometry(mtq_c), add = TRUE, cex = 1.2, col = "red", pch = 20)

Distance Matrix

mat <- st_distance(x = mtq_c, y = mtq_c)
mat[1:5, 1:5]

Units: m
          [,1]     [,2]      [,3]      [,4]      [,5]
[1,]     0.000 35297.56  3091.501 12131.617 17136.310
[2,] 35297.557     0.00 38332.602 25518.913 18605.249
[3,]  3091.501 38332.60     0.000 15094.702 20226.198
[4,] 12131.617 25518.91 15094.702     0.000  7177.011
[5,] 17136.310 18605.25 20226.198  7177.011     0.000

Polygons Aggregation

Simple union:

mtq_u <- st_union(mtq)
plot(st_geometry(mtq), col = "lightblue")
plot(st_geometry(mtq_u), add = T, lwd = 2, border = "red")

Aggregation according to a grouping variable:

library(dplyr)
mtq_u2 <- mtq %>% group_by(STATUT) %>% summarize(P13_POP = sum(P13_POP))
plot(st_geometry(mtq), col = "lightblue")
plot(st_geometry(mtq_u2), add = T, lwd = 2, border = "red", col = NA)

Buffer Zone

mtq_b <- st_buffer(x = mtq_u, dist = 5000)
plot(st_geometry(mtq), col = "lightblue")
plot(st_geometry(mtq_u), add = T, lwd = 2)
plot(st_geometry(mtq_b), add = T, lwd = 2, border = "red")

Polygon Intersection

m <- rbind(c(700015, 1624212), c(700015, 1641586), c(719127, 1641586), c(719127, 
    1624212), c(700015, 1624212))
p <- st_sf(st_sfc(st_polygon(list(m))), crs = st_crs(mtq))
plot(st_geometry(mtq))
plot(p, border = "red", lwd = 2, add = T)

mtq_z <- st_intersection(x = mtq, y = p)
plot(st_geometry(mtq))
plot(st_geometry(mtq_z), col = "red", border = "green", add = T)

Voronoi Polygons

google: “st_voronoi R sf” (https://github.com/r-spatial/sf/issues/474 & https://stackoverflow.com/questions/45719790/create-voronoi-polygon-with-simple-feature-in-r)

mtq_v <- st_voronoi(x = st_union(mtq_c))
mtq_v <- st_intersection(st_cast(mtq_v), st_union(mtq))
mtq_v <- st_join(x = st_sf(mtq_v), y = mtq_c, join = st_intersects)
mtq_v <- st_cast(mtq_v, "MULTIPOLYGON")
plot(st_geometry(mtq_v), col = "lightblue")

Maps with R

Several solutions are available:

ggplot2 users can have a look to ggplot2 mapping features (geom_sf) that can mix nicely with ggspatial.
For more advanced mapping features in a ggplot2-like syntax have a look to tmap
cartography is based on base graphics and allow most of basic and advanced cartographic representations. Full disclosure: the speaker is the maintainer of cartography.

Here we will focus on cartography and do small examples with ggplot2.

`cartography`

Data Preparation

library(sf)
# Import geo layer
sm <- st_read(dsn = "../data/rhone/seine_maritime.geojson", stringsAsFactors = F, 
    quiet = TRUE)
dep <- st_read(dsn = "../data/rhone/dep.geojson", stringsAsFactors = F, quiet = TRUE)
# change projection (lambert93)
sm <- st_transform(sm, 2154)
dep <- st_transform(dep, 2154)

# Import dataset
csp <- read.csv("../data/rhone/data_seine_maritime.csv")
# merge geolayer and dataset
sm <- merge(sm, csp, by = "INSEE_COM", all.x = TRUE)

Proportional symbols

library(cartography)

plot(st_geometry(sm))
propSymbolsLayer(sm, var = "act")
title("Active Population")

# Custom map of active population
par(mar = c(0.2, 0.2, 1.4, 0.2), bg = "azure")
bb <- st_bbox(sm)
plot(st_geometry(dep), col = "ivory", border = "ivory3", xlim = bb[c(1, 3)], 
    ylim = bb[c(2, 4)])
plot(st_geometry(sm), col = "cornsilk2", border = NA, lwd = 0.5, add = T)
propSymbolsLayer(sm, var = "act", col = "darkblue", inches = 0.5, border = "white", 
    lwd = 0.7, symbols = "square", legend.style = "e", legend.pos = "topleft", 
    legend.title.txt = "Labor Force\n(2014)", legend.values.rnd = 0)
barscale(size = 10)
north(pos = "topright", col = "darkblue")
layoutLayer(title = "Workforce in Seine-Maritime", sources = "Insee, 2018", 
    author = "Kim & Tim, 2018", col = "darkblue", coltitle = "white", frame = TRUE, 
    scale = NULL, north = FALSE)

Typology Map

par(mar = c(0.2, 0.2, 1.4, 0.2), bg = "azure")
plot(st_geometry(dep), col = "ivory", border = "ivory3", xlim = bb[c(1, 3)], 
    ylim = bb[c(2, 4)])
typoLayer(sm, var = "cat", border = "ivory", lwd = 0.5, legend.values.order = c("agr", 
    "art", "cad", "int", "emp", "ouv"), col = c("#e3b4a2", "#a2d5d6", "#debbd4", 
    "#b5dab6", "#afc2e3", "#e9e2c1"), add = TRUE, legend.pos = "n")

legendTypo(title.txt = "Dominant socio-professional Category", col = c("#e3b4a2", 
    "#a2d5d6", "#debbd4", "#b5dab6", "#afc2e3", "#e9e2c1"), categ = c("Agriculteurs", 
    "Artisans", "Cadres", "Prof. Inter.", "Employés", "Ouvriers"), nodata = F)
barscale(size = 10)
north(pos = "topright", col = "darkblue")
layoutLayer(title = "Workforce Distribution in Seine-Maritime", sources = "Insee, 2018", 
    author = "Kim & Tim, 2018", col = "darkblue", coltitle = "white", frame = TRUE, 
    scale = NULL, north = FALSE)

Choropleth Map

sm$pcad <- 100 * sm$cad/sm$act

bks <- getBreaks(v = sm$pcad, method = "quantile", nclass = 6)
cols <- carto.pal("green.pal", 3, "wine.pal", 3)
par(mar = c(0.2, 0.2, 1.4, 0.2), bg = "azure")
plot(st_geometry(dep), col = "ivory", border = "ivory3", xlim = bb[c(1, 3)], 
    ylim = bb[c(2, 4)])
choroLayer(sm, var = "pcad", breaks = bks, col = cols, border = "grey80", lwd = 0.4, 
    legend.pos = "topleft", legend.title.txt = "Share of managers (%)", add = T)
layoutLayer(title = "Managers", sources = "Insee, 2018", author = "Kim & Tim, 2018", 
    theme = "green.pal", col = "darkred", coltitle = "white", postitle = "center", 
    frame = TRUE, scale = 10)
north(pos = "topright", south = TRUE)

library(cartogram)
sm_c1 <- cartogram_cont(sm, "act", 3)
sm$pcad <- 100 * sm$cad/sm$act

bks <- getBreaks(v = sm$pcad, method = "quantile", nclass = 6)
cols <- carto.pal("green.pal", 3, "wine.pal", 3)
par(mar = c(0.2, 0.2, 1.4, 0.2), bg = "azure")
plot(st_geometry(dep), col = "ivory", border = "ivory3", xlim = bb[c(1, 3)], 
    ylim = bb[c(2, 4)])
choroLayer(sm_c1, var = "pcad", breaks = bks, col = cols, border = "grey80", 
    lwd = 0.4, legend.pos = "topleft", legend.title.txt = "Share of managers (%)", 
    add = T)
layoutLayer(title = "Managers", sources = "Insee, 2018", author = "Kim & Tim, 2018", 
    theme = "green.pal", col = "darkred", coltitle = "white", postitle = "center", 
    frame = TRUE, scale = 10)
north(pos = "topright", south = TRUE)

Gridded Map

These maps may allow to hide or, at least, diminish the MAUP.

sqrt(quantile(st_area(sm), 0.9))

3904.689 m

grid <- getGridLayer(x = sm, cellsize = 3900 * 3900, type = "regular", var = c("cad", 
    "act"))
grid$pcad <- 100 * grid$cad/grid$act
par(mar = c(0.2, 0.2, 1.4, 0.2), bg = "azure")
plot(st_geometry(dep), col = "ivory", border = "ivory3", xlim = bb[c(1, 3)], 
    ylim = bb[c(2, 4)])
choroLayer(grid, var = "pcad", breaks = bks, col = cols, border = "grey80", 
    lwd = 0.4, legend.pos = "topleft", legend.title.txt = "Share of managers\n(en %)", 
    add = T)
layoutLayer(title = "Managers", sources = "Insee, 2018", author = "Kim & Tim, 2018", 
    theme = "green.pal", col = "darkred", coltitle = "white", postitle = "center", 
    frame = TRUE, scale = 10)
north(pos = "topright", south = TRUE)

Smoothed Map

grid$cad100 <- grid$cad * 100
par(mar = c(0.2, 0.2, 1.4, 0.2), bg = "azure")
plot(st_geometry(dep), col = "ivory", border = "ivory3", xlim = bb[c(1, 3)], 
    ylim = bb[c(2, 4)])
smoothLayer(x = grid, var = "cad100", var2 = "act", typefct = "exponential", 
    span = 4000, beta = 2, breaks = bks, col = cols, legend.pos = "topleft", 
    mask = st_buffer(sm, 0), legend.title.txt = "Share of managers* (%)", border = "grey90", 
    lwd = 0.2, add = T)
layoutLayer(title = "Managers", sources = "Insee, 2018", author = "Kim & Tim, 2018", 
    theme = "green.pal", col = "darkred", coltitle = "white", postitle = "center", 
    frame = TRUE, scale = 10)
north(pos = "topright", south = TRUE)
text(x = 518000, y = 6921123, font = 3, cex = 0.8, labels = "*Potential smoothing\n exponential function\n span = 2.5km, beta = 2")

`ggplot2`

Proportional symbols layer

library(ggplot2)

ggplot() +
  geom_sf(data = dep, colour = "ivory3",fill = "ivory") +
  geom_sf(data = sm %>%  st_centroid(),
          
          aes(size= cad), colour="#E84923CC", show.legend = 'point') +
  scale_size(name = "Active population",
             breaks = c(100,1000,5000),
             range = c(0,20)) +
  coord_sf(crs = 2154, datum = NA,
           xlim = st_bbox(sm)[c(1,3)],
           ylim = st_bbox(sm)[c(2,4)]
  ) +
  theme_minimal() +
  theme(panel.background = element_rect(fill = "azure",color=NA)) +
  labs(title = "Active population",
       caption = "Insee, 2018\nKim & Tim, 2018")

Choropleth layer

ggplot() +
  geom_sf(data = dep, colour = "ivory3",fill = "ivory") +
  geom_sf(data = sm, aes(fill = pcad), colour = "grey80") +
  scale_fill_gradientn(name = "Share of managers (%)",
                       
                       colours = carto.pal("green.pal", 3,"wine.pal",3),
                       values=bks/max(bks))+
  coord_sf(crs = 2154, datum = NA,
           xlim = st_bbox(sm)[c(1,3)],
           ylim = st_bbox(sm)[c(2,4)]
  ) +
  theme_minimal() +
  theme(panel.background = element_rect(fill = "azure",color=NA)) +
  labs(title = "Managers",
       caption = "Insee, 2018\nKim & Tim, 2018")

Exploration of SIRENE & OSM databases for restaurants

CRAN Task View: Analysis of Spatial Data

See file data_prep.R for data extraction.

# spatial data management
library(sf)
# cartography
library(cartography)
# smooth density computation
library(spatstat)
library(raster)
library(maptools)
# interactive mapping
library(mapview)

Display Points

# Load data
adm <- readRDS("../data/iris_p13.rds")
feat_sir <- readRDS("../data/sir_p13.rds")
feat_osm <- readRDS("../data/osm_p13.rds")

# Define margins
par(mar = c(0, 0, 1.2, 0), mfrow = c(1, 2))

# Plot the maps
plot(st_geometry(adm), col = "ivory1", border = "ivory3", lwd = 0.5, bg = "#FBEDDA")
plot(st_geometry(feat_sir), col = "red", pch = 20, add = T, cex = 0.5)
layoutLayer(title = "SIR", sources = paste0(nrow(feat_sir), " restaurants"), 
    author = "Kim & Tim, 2018", scale = NULL, frame = FALSE, tabtitle = TRUE)
legend(x = "topright", legend = "= 1 restaurant", pch = 20, pt.cex = 0.5, bty = "n", 
    cex = 0.7, col = "red")

plot(st_geometry(adm), col = "ivory1", border = "ivory3", lwd = 0.5, bg = "#FBEDDA")
plot(st_geometry(feat_osm), col = "red", pch = 20, add = T, cex = 0.5)
layoutLayer(title = "OSM", sources = paste0(nrow(feat_osm), " restaurants"), 
    author = "Kim & Tim, 2018", scale = 0.5, north = T, frame = FALSE, tabtitle = TRUE)

Interactive Visualisation

Explore datasets interactively

The default is not bad:

mapview(feat_sir) + mapview(feat_osm, col.regions = "red")

mapview allows highly customizable maps:

mapview(feat_sir, map.types = "OpenStreetMap", col.regions = "#940000", label = paste(feat_sir$L2_NORMALISEE, 
    feat_sir$NOMEN_LONG, sep = " - "), color = "white", legend = TRUE, layer.name = "SIRENE", 
    homebutton = FALSE, lwd = 0.5) + mapview(feat_osm, col.regions = "#000094", 
    color = "white", legend = TRUE, label = feat_osm$name, lwd = 0.5, layer.name = "OSM", 
    homebutton = FALSE)

These maps, as appealing as they seem to be, are not really suitable for displaying geostatistical information.

Nonetheless they can be really useful for exploratory data analysis.

Count Points in Units

In administrative units

# Intersect adm and feat
inter_osm <- st_intersects(adm, feat_osm)
inter_sir <- st_intersects(adm, feat_sir)
# Count points in polygons
adm <- st_sf(adm[, 1:2, drop = T], n_osm = sapply(X = inter_osm, FUN = length), 
    n_sir = sapply(X = inter_sir, FUN = length), geometry = st_geometry(adm))
# Display the map
par(mar = c(0, 0, 1.2, 0), mfrow = c(1, 2))
plot(st_geometry(adm), col = "ivory1", border = "ivory3", lwd = 0.5, bg = "#FBEDDA")
propSymbolsLayer(adm, var = "n_sir", inches = 0.1)
layoutLayer(title = "SIR", sources = "", author = "", scale = NULL, tabtitle = TRUE, 
    frame = FALSE)
# Display the map
plot(st_geometry(adm), col = "ivory1", border = "ivory3", lwd = 0.5, bg = "#FBEDDA")
propSymbolsLayer(adm, var = "n_osm", inches = 0.1)
layoutLayer(title = "OSM", sources = "", author = "", scale = 0.5, north = T, 
    tabtitle = TRUE, frame = FALSE)

In a regular grid

Create a small function that builds a regular grid and counts points in each cell.

pt_in_grid <- function(feat, adm, cellsize = 50) {
    # Create a regular grid (adm bbox)
    grid <- st_make_grid(x = adm, cellsize = cellsize, what = "polygons")
    
    # Keep only cells that intersect adm
    . <- st_intersects(grid, adm)
    grid <- grid[sapply(X = ., FUN = length) > 0]
    
    # Count pts in grid
    . <- st_intersects(grid, feat)
    grid <- st_sf(n = sapply(X = ., FUN = length), grid)
    
    return(grid)
}

Create a function that plots a map

plot_grid <- function(grid, adm, title, bks, col) {
    plot(st_geometry(adm), col = "ivory1", border = "ivory3", lwd = 0.5)
    choroLayer(grid, var = "n", border = NA, add = TRUE, breaks = bks, col = cols, 
        legend.pos = "n")
    layoutLayer(title = title, scale = NULL, frame = FALSE, tabtitle = TRUE, 
        author = "", sources = "")
}

Build grids and display maps

# plot 6 maps on a single figure
par(mar = c(0, 0, 1.8, 0), mfrow = c(2, 3), bg = "#FBEDDA", ps = 16)

# defines a unique set of breaks for all maps
bks <- seq(1, 22, 3)
cols <- carto.pal("sand.pal", length(bks) - 1)

# SIR maps 50 m cells
grid <- pt_in_grid(feat_sir, adm, 50)
plot_grid(grid = grid, adm = adm, title = "SIR - 50 m cells", col = cols, bks = bks)

# 100 m cells
grid <- pt_in_grid(feat_sir, adm, 100)
plot_grid(grid = grid, adm = adm, title = "SIR - 100 m cells", col = cols, bks = bks)

# 150 m cells
grid <- pt_in_grid(feat_sir, adm, 150)
plot_grid(grid = grid, adm = adm, title = "SIR - 150 m cells", col = cols, bks = bks)

# Add a north arrow
north()

# OSM maps 50 m cells
grid <- pt_in_grid(feat_osm, adm, 50)
plot_grid(grid = grid, adm = adm, title = "OSM - 50 m cells", col = cols, bks = bks)

# Add sources
mtext(text = "Map data © OpenStreetMap contributors, under CC BY SA.\nSIRENE - 2018, INSEE - 2018", 
    side = 1, line = -1, cex = 0.5, adj = 0)

# 100 m cells
grid <- pt_in_grid(feat_osm, adm, 100)
plot_grid(grid = grid, adm = adm, title = "OSM - 100 m cells", col = cols, bks = bks)

# 150 cells
grid <- pt_in_grid(feat_osm, adm, 150)
plot_grid(grid = grid, adm = adm, title = "OSM - 150 m cells", col = cols, bks = bks)

# Add legend
legendChoro(pos = "topright", title.cex = 0.7, values.cex = 0.5, title.txt = "N. restaurants", 
    breaks = bks, nodata = FALSE, values.rnd = 0, col = cols)

# Add scalebar
barscale(1)

Smooth Density Analysis

Define a function that computes smoothed restaurant density (KDE method).

compute_kde <- function(feat, adm, title, sigma = 100, res = 50) {
    # Define an observation window
    w <- as.owin(as(adm, "Spatial"))
    # sf to coords
    pts <- st_coordinates(feat)
    # Coords to ppp
    p <- ppp(pts[, 1], pts[, 2], window = w)
    # Compute KDE
    dens <- density.ppp(p, sigma = sigma, eps = res)
    # Image to raster (+ proj & km2)
    result <- raster(dens, crs = st_crs(adm)[[2]]) * 1e+06
    return(result)
}

Define a function that maps the results

plot_kde <- function(x, adm, method = "equal", nclass = 12, title = "", author = "", 
    sources = "", scale = NULL, legend.title = "Density\n(n/km2)", legend.pos = "topright", 
    values.rnd = 0) {
    # compute breaks
    bks <- unique(getBreaks(values(x), nclass = nclass, method = method))
    # Color ramp
    cols <- (mapview::mapviewGetOption("raster.palette"))(length(bks) - 1)
    # Plot the map
    plot(st_geometry(adm), col = NA, border = NA, main = "", bg = "#FBEDDA")
    plot(x, breaks = bks, col = cols, add = T, legend = F)
    legendChoro(pos = legend.pos, title.txt = legend.title, values.cex = 0.5, 
        breaks = bks, nodata = FALSE, values.rnd = values.rnd, col = cols)
    layoutLayer(title = title, scale = scale, tabtitle = TRUE, frame = FALSE, 
        author = author, sources = sources)
}

# Plot 6 maps on a single figure
par(mar = c(1, 0, 1.8, 0), mfrow = c(2, 3), bg = "#FBEDDA", ps = 16)

x <- compute_kde(feat = feat_sir, adm = adm, sigma = 50, res = 20)
plot_kde(x, adm, title = "SIR - Sigma = 50", legend.title = "Restaurants\n/km2")
x <- compute_kde(feat = feat_sir, adm = adm, sigma = 100, res = 20)
plot_kde(x, adm, title = "SIR - Sigma = 100", legend.title = "Restaurants\n/km2")
x <- compute_kde(feat = feat_sir, adm = adm, sigma = 250, res = 20)
plot_kde(x, adm, title = "SIR - Sigma = 250", legend.title = "Restaurants\n/km2")
x <- compute_kde(feat = feat_osm, adm = adm, sigma = 50, res = 20)
plot_kde(x, adm, title = "OSM - Sigma = 50", legend.title = "Restaurants\n/km2")
x <- compute_kde(feat = feat_osm, adm = adm, sigma = 100, res = 20)
plot_kde(x, adm, title = "OSM - Sigma = 100", legend.title = "Restaurants\n/km2")
x <- compute_kde(feat = feat_osm, adm = adm, sigma = 250, res = 20)
plot_kde(x, adm, title = "SIR - Sigma = 250", legend.title = "Restaurants\n/km2")

reproducibility

sessionInfo()

R version 3.3.2 (2016-10-31)
Platform: x86_64-w64-mingw32/x64 (64-bit)
Running under: Windows 7 x64 (build 7601) Service Pack 1

locale:
[1] LC_COLLATE=French_France.1252  LC_CTYPE=French_France.1252   
[3] LC_MONETARY=French_France.1252 LC_NUMERIC=C                  
[5] LC_TIME=French_France.1252    

attached base packages:
[1] stats     graphics  grDevices utils     datasets  methods   base     

other attached packages:
 [1] mapview_2.3.0         maptools_0.9-2        spatstat_1.56-1      
 [4] rpart_4.1-10          nlme_3.1-128          spatstat.data_1.3-1  
 [7] ggplot2_3.0.0         SpatialPosition_1.2.0 raster_2.6-7         
[10] sp_1.2-5              cartogram_0.1.0       cartography_2.1.1    
[13] dplyr_0.7.4           sf_0.6-3              rmdformats_0.3.3     
[16] knitr_1.20           

loaded via a namespace (and not attached):
 [1] viridisLite_0.3.0    foreach_1.4.3        R.utils_2.5.0       
 [4] shiny_1.0.5          assertthat_0.2.0     highr_0.6           
 [7] stats4_3.3.2         yaml_2.1.18          pillar_1.1.0        
[10] lattice_0.20-34      glue_1.2.0           digest_0.6.15       
[13] polyclip_1.9-1       colorspace_1.3-2     htmltools_0.3.6     
[16] httpuv_1.3.5         Matrix_1.2-7.1       R.oo_1.21.0         
[19] plyr_1.8.4           pkgconfig_2.0.1      questionr_0.6.2     
[22] bookdown_0.5         xtable_1.8-2         webshot_0.5.0       
[25] scales_0.5.0.9000    tensor_1.5           satellite_1.0.1     
[28] spatstat.utils_1.9-0 tibble_1.4.2         mgcv_1.8-15         
[31] withr_2.1.2          lazyeval_0.2.1       gdalUtils_2.0.1.7   
[34] magrittr_1.5         mime_0.5             deldir_0.1-14       
[37] evaluate_0.10.1      R.methodsS3_1.7.1    foreign_0.8-67      
[40] class_7.3-14         tools_3.3.2          formatR_1.5         
[43] stringr_1.3.1        munsell_0.4.3        bindrcpp_0.2        
[46] e1071_1.6-8          rlang_0.2.1          classInt_0.1-24     
[49] units_0.6-0          grid_3.3.2           iterators_1.0.8     
[52] rstudioapi_0.7       htmlwidgets_1.2      goftest_1.1-1       
[55] crosstalk_1.0.0      miniUI_0.1.1         labeling_0.3        
[58] base64enc_0.1-3      rmarkdown_1.10.12    gtable_0.2.0        
[61] codetools_0.2-15     abind_1.4-5          DBI_1.0.0           
[64] R6_2.2.2             rgdal_1.2-11         rgeos_0.3-24        
[67] bindr_0.1            stringi_1.1.7        htmldeps_0.1.1      
[70] Rcpp_0.12.16         png_0.1-7            leaflet_1.1.0

Geovisualization and Spatial Analysis